Edge computing systems struggle to efficiently manage multiple concurrent deep neural network (DNN) workloads while meeting strict latency requirements, minimizing power consumption, and maintaining environmental sustainability. This paper introduces Ecomap, a sustainability-driven framework that dynamically adjusts the maximum power threshold of edge devices based on real-time carbon intensity. Ecomap incorporates the innovative use of mixed-quality models, allowing it to dynamically replace computationally heavy DNNs with lighter alternatives when latency constraints are violated, ensuring service responsiveness with minimal accuracy loss. Additionally, it employs a transformer-based estimator to guide efficient workload mappings. Experimental results using NVIDIA Jetson AGX Xavier demonstrate that Ecomap reduces carbon emissions by an average of 30% and achieves a 25% lower carbon delay product (CDP) compared to state-of-the-art methods, while maintaining comparable or better latency and power efficiency.